How can I get these mesh information for exporting?
Vertices are shared, no matter what material etc. the using polygons have. 

Per-face vertex data is stored in loops (C.object.data.loops).

The elements of C.object.data.uv_layers[#].data[#] correspond to loop indexes. The first UV coordinate of the active UV map can be retrieved like .uv_layers.active.data[0].uv.

I'm not sure if triangle stripes and fans are still used nowadays. If a game-engine handles vertices like Blender and shares them among faces, there's no real difference in memory consumption...

You may wanna use the Separate P operator and split a mesh by material. Or create a lookup dictionary from material assignments to efficiently retrieve the right polygons.

Elements in C.object.data.uv_textures[#].data[#] correspond to face indexes, e.g. .uv_textures.active.data[0].image for polygons[0]. Note that the image attribute is set via UV / Image Editor, but that there's a second type of material assignment - the one from Material tab in Properties Editor, which sets polygons[#].material_index (just an interger, which is the index of the material in C.object.data.materials[#].